In recent years, many methods for subband or wavelet compression of images have been proposed. One such method is the JPEG2000 image compression standard, as described in “Information Technology—JPEG2000 Image Coding System, ISO/IEC International Standard 15444-1, ITU Recommendation T.800”. The JPEG2000 standard is based on the EBCOT algorithm as described by Taubman (David Taubman, “High performance scalable compression with EBCOT,” IEEE Transactions on Image Processing, 9(7), pp. 1158-1170, July 2000). The JPEG2000 encoder decomposes the image into a collection of subbands. Each subband is divided into rectangular blocks called codeblocks. Codeblocks are quantized and entropy coded independently in a number of coding passes. The compressed coding passes from each codeblock of each subband are aggregated to form quality layers. Each quality layer contains compressed data corresponding to a whole number of coding passes from each codeblock of each subband. A codeblock may contribute zero or more coding passes to a given layer. Adding more layers to the compressed bit-stream generally improves the visual quality of the reconstructed image while increasing the bit-rate. The JPEG2000 standard provides a very flexible framework for organizing and ordering the compressed bit-stream. For each layer, it is the responsibility of the encoder to determine how many coding passes from each codeblock will be included in that layer.
Taubman describes a method for the formation of layers in a JPEG2000 encoder. In his method, mean squared error (MSE) or visually weighted MSE is used as the distortion metric. Each subband is quantized using a very small step-size to produce many more coding passes than would be included in the final compressed bit-stream. Then, post-compression rate-distortion optimization is used to decide which coding passes should be discarded altogether, and also to decide how the layers are formed. Specifically, each layer contains coding passes that yield the greatest reduction in distortion for a given rate constraint. Once the encoding is complete, the rate-distortion information used in the layer formation process is discarded.
The loss of rate-distortion information leads to two limitations of this layer formation and encoding method. One limitation is that it may not be possible to transcode the compressed image to a lower bit-rate (possibly at a reduced resolution) in an optimal manner. If the transcoding request is made for the compressed image at a resolution and bit-rate that does not correspond to a layer boundary, the resulting transcoded data contains a partial layer and is suboptimal in terms of MSE or weighted MSE performance.
A second limitation is that when visual weights are used, layers are formed with respect to a specific visually weighted MSE distortion metric. However, the resulting order of the compressed bit-stream may be sub-optimal, if the image is to be transcoded using a different set of visual weights.